The present embodiments relate to a method and a control sequence determination device for determining a magnetic resonance system control sequence that includes a multi-channel pulse with a plurality of individual high frequency (HF) pulses to be transmitted in parallel by the magnetic resonance system via different independent high-frequency transmission channels. A multi-channel pulse is calculated based on an MR excitation quality parameter in an HF pulse optimization method. In one embodiment, an HF pulse of the multi-channel pulse to be transmitted on a transmission channel includes a plurality of successive HF partial pulses in very short, discrete time steps. The present embodiments further relate to a method for operating a magnetic resonance system that includes a plurality of independent high-frequency transmission channels using such a magnetic resonance system control sequence. The present embodiments further relate to a magnetic resonance system that includes a plurality of independent high-frequency transmission channels and a control device configured to transmit, via the different high-frequency transmission channels, a multi-channel pulse having a plurality of parallel individual HF pulses in order to carry out a desired measurement based on a predetermined control sequence.
In a magnetic resonance system, the body to be examined is generally subjected to a relatively high main magnetic field via a main field magnetic system (i.e., the so-called Bo field, of, for example 3 or 7 Tesla). Additionally, a magnetic field gradient is applied using a gradient system. Then, using suitable antenna devices, high-frequency excitation signals (HF signals) are transmitted via a high-frequency transmission system. The high-frequency transmission system is intended to cause the nuclear spins of specific atoms resonantly excited by the high-frequency field to be tilted in a spatially resolved manner by a defined flip angle relative to the magnetic field lines of the main magnetic field. The high-frequency magnetic field, which is transmitted in the form of individual pulses or pulse trains, may be denoted as the B 1 field. Magnetic resonance excitation (MR excitation) using magnetic high-frequency pulses and/or the resulting flip angle distribution is referred to hereinafter as nuclear magnetization or “magnetization” for short. During the relaxation of the nuclear spins, high-frequency signals (so-called magnetic resonance signals), are emitted. The high-frequency signals are received by suitable receiver antennas and are then processed further. The desired image data may then be reconstructed from the acquired raw data. The high-frequency signals for the nuclear spin magnetization are generally transmitted by or using a so-called “whole body coil” or “bodycoil.” A typical design of a body coil is a birdcage antenna, which consists of a plurality of transmission rods that are arranged to extend parallel to the longitudinal axis around a patient area of the tomograph in which a patient is located during the examination. On the front face, each of the antenna rods are capacitively connected together in an annular manner. The magnetic resonance signals are generally received by local coils in the vicinity of the body, but may, alternatively or additionally, be received by the bodycoil. The local coils are frequently used for transmitting MT excitation signals.
Hitherto, it was typical to operate whole body antennas in a “homogenous mode” (e.g., a “CP mode”). Accordingly, a single temporal HF signal is provided with a defined fixed phase and amplitude ratio relative to all components of the transmission antennas, such as, for example, all transmission rods of a birdcage antenna. In more modern magnetic resonance systems, it has become possible to provide the individual transmission channels (e.g., the individual rods of a birdcage antenna) with individual HF signals. Accordingly, a multi-channel pulse is transmitted which, as described above, includes a plurality of individual high-frequency pulses. The individual high-frequency pulses may be transmitted in parallel via the different independent high-frequency transmission channels. Because the individual pulses are transmitted in parallel, a multi-channel pulse (i.e., the pTX pulse“) is formed. The multi-channel pulse may, for example, be used as an excitation, refocusing and/or inversion pulse. An antenna system that includes a plurality of independently controllable antenna components and/or transmission channels is often also denoted as “transmit array,” regardless of whether the transmit array is a whole body antenna or an antenna array in the vicinity of the body.
Such pTX pulses and/or pulse trains, which are constructed therefrom, are determined for a specific planned measurement. This is usually done in advance by establishing the pulse shape and phase of the pulses that are to be transmitted on the individual transmission channels. As a result, the HF pulses for the individual transmission channels are determined over time, as a function of a “transmission k-space gradient trajectory, in an optimization method. The “transmission k-space gradient trajectory” (“gradient trajectory”), is generally predetermined by a measurement protocol. The gradient trajectory refers to the coordinates in the k-space that are reached by setting the individual gradients at specific times, or, in other words, the coordinates in the k-space that are reached using gradient pulse trains (with appropriate x-, y- and z-gradient pulses) to be transmitted in a coordinated manner that is appropriate for each of the HF pulse trains. The k-space is the spatial frequency domain and the gradient trajectory in the k-space describes the path on which the k-space is traversed in terms of time when an HF pulse and/or the parallel pulses are transmitted by a corresponding switching of the gradient pulses. By setting the gradient trajectory in the k-space (i.e. by setting the appropriate gradient trajectory applied in parallel with the multi-channel pulse train), the spatial frequencies at which specific HF energies are deposited may be determined.
When planning the HF pulse sequence, the user specifies an MR excitation quality parameter (e.g., a parameter in the form of a target magnetization). The user may, for example, specify a desired spatially resolved flip angle distribution that is used as a reference value within a target function. In an optimization program, the appropriate HF pulses are thus calculated for the individual channels, such that the specified MR excitation quality parameter is achieved. The MR excitation quality parameter is based on the Bloch equation:
                                                        ⅆ              m                                      ⅆ              t                                =                                    γ              ·              m                        ×            B                          ⁢                                                      (        1        )            The Bloch equation generally describes the magnetization structure by a magnetization vector m in a magnetic field B, where γ is the gyromagnetic ratio of the core to be excited (for the generally excited hydrogen γ=42.58 MHz/T).
As noted above, the pulse shape is generally calculated so that a pulse with a specific length is discretized in a number of very short time steps. Typically, the time steps are of a 1 to 10 μs duration. A HF pulse of, for example, 10 to 20 ms duration thus contains over 1000 time steps. Within each time step, it may be roughly assumed that the pulse value of the HF pulse to be transmitted is constant. For small flip angles (e.g., flip angles below ca. 5°) the Bloch equation may, as a result, be described by a linear approximation based on an approximation of the first-order Taylor approximation:m=J·b   (2)
In equation (2), m represents the vector of the spatially discretized (transverse) magnetization, J represents the Jacobi matrix of the magnetization m, and the vector b represents the temporal discretization of the HF pulses, i.e., b=(b1, b2, . . . , bj, . . . , bn), where bj is a pulse value at the time and/or in the time step j=1, . . . , n. The pulse values are generally complex and each pulse contains a real and imaginary part which represent the voltage amplitude and the phase of the HF pulse. The elements aij of the Jacobi matrix J may, according to Grissom et al., “Spatial Domain Method for the Design of RF Pulses in Multicoil Parallel Excitation,” Mag. Res. Med. 56, 620-629, 2006, be approximately described by the equationaij=iγΔteiγΔB0(xi)(tj−T)eixikj  (3),where xi represents the local vector of a voxel with the index i of an excitation volume, kj represents the location frequency vector in the k-space at the time step j, ΔB0 represents the local deviation of the magnetic field from the desired B0 field at the location xi, tj represents the time for the discrete time step j, and T represents the total pulse length. The letter i, which is not in the index, represents the usual imaginary unit.
The solution of the linear equation system defined in such a manner thus provides, for each of the time steps j=1, . . . n, a complex pulse value and, in turn, the voltage amplitude and the phase of the pulse in this time step for the control of the magnetic resonance system.
Generally, the solution is approximated as much as possible in an optimization method with a target function that is to be minimized and that corresponds to equation (2). The pulse values for the individual time steps of the pulses are thus the degrees of freedom and/or variables of the target function to be optimized. When using an LSQR optimization method (see, for example, C. C. Paige and M. A. Saunders, “LSQR: an algorithm for sparse linear equations and sparse least squares,” TOMS 8(1), 43-71 (1982), or C. C. Paige and M. A. Saunders, Algorithm 583; “LSQR: Sparse linear equations and least square problems,” TOMS 8(2), 195-209 (1982) the target function may, for example, be expressed as follows:min∥m−mdes∥22=min∥J·b−mdes∥22   (4),where mdes is the desired target magnetization. The value of a vector is, in equation (4), understood in terms of components. The norm selected here is, as an example, the Euclidian norm (L2-norm). If a further optimization algorithm (e.g., a magnitude least square method (MLS method) is used, a similar target function adapted to the method is used.
For a specific measurement, the different multi-channel pulses and/or pulse trains of the pulses are thus determined, the gradient pulse trains belonging to the respective control sequence and further control parameters are defined in a so-called measurement protocol. The measurement protocol is produced in advance and may be retrieved from a memory, for example, for a specific measurement, and optionally modified by the operator. During the measurement process, the magnetic resonance system is automatically and fully controlled based on this measurement protocol. The control device of the magnetic resonance system reads out the commands from the measurement protocol and processes the commands. The calculated pulse shapes are thus initially generated, in digital form, in a small signal generator of the respective transmission channel. The pulse shapes are subsequently converted into an analog signal and boosted using a high-frequency booster, such that a sufficiently high transmission pulse with the desired pulse shape is present. The pulse may then be stored in the antenna element belonging to the respective transmission channel.
Locating the optimal pulse b in order to achieve, as easily as possible, a specific target magnetization, results in a more complex computation, as more free variables have to be solved within the optimization problem according to equation (4). For example, the number of time steps required to generate a pulse of a specific temporal length T may substantially increase the complexity of the computation. Typically, time steps of between 1 and 10 μs duration are used, such that a pulse of, for example, 10 to 20 ms duration contains approximately 1000 to 2000 time steps. Consequently, in an optimization method for a multi-channel pulse for a magnetic resonance system with eight independent transmission channels, 8000 to 16000 variables are simultaneously be considered. As the number of transmission channels increases, the number of variables also increases. In turn, the required computing time increases proportionally as well.
One possibility for reducing the number of degrees of freedom would be to make the time steps longer. However, it has been shown that, when the time steps are lengthened and the optimal pulses are located using the above-described linear approximation, the subsequent transmission of the pulses no longer results in the desired magnetization. Thus, by lengthening the time steps, it is no longer possible to utilize a linear equation system. Instead, pulse calculation methods that are more complex and, thus, more time-consuming to compute would have to be used. Additionally, in practice, it has been shown that the above-described linear method is no longer sufficiently accurate when higher gradient field strengths are present. On the other hand, it is advantageous to use higher gradient field strengths because this allows the k-space to be transmited more rapidly and may allow for a shorter measuring time.